Oh, sorry - but I don't believe magazines have a sample button. If you look at your picture, it does say, in the middle, that you can try the Times for a 30-day trial period (free).
Sorry for the confusion. My advice was only for ebooks, as twerppoet had already mentioned magazines and such didn't usually have a free sample - only trial periods.
So, you'll have to subscribe to this magazine/paper and try it. If you don't like it, you'll have to make sure to cancel the subscription BEFORE the trial period is up.
Marilyn